Nuprl Lemma : fpf-dom-compose
∀[x:Top]. ∀[f:a:Top fp-> Top]. ∀[g,eq:Top]. (x ∈ dom(g o f) ~ x ∈ dom(f))
Proof
Definitions occuring in Statement :
fpf-compose: g o f,
fpf-dom: x ∈ dom(f),
fpf: a:A fp-> B[a],
uall: ∀[x:A]. B[x],
top: Top,
sqequal: s ~ t
Definitions unfolded in proof :
all: ∀x:A. B[x],
member: t ∈ T,
top: Top,
uall: ∀[x:A]. B[x],
so_lambda: λ2x.t[x],
so_apply: x[s]
Lemmas referenced :
fpf_dom_compose_lemma,
top_wf,
fpf_wf
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
cut,
lemma_by_obid,
sqequalHypSubstitution,
sqequalTransitivity,
computationStep,
dependent_functionElimination,
thin,
isect_memberEquality,
voidElimination,
voidEquality,
hypothesis,
isect_memberFormation,
introduction,
sqequalAxiom,
isectElimination,
hypothesisEquality,
because_Cache,
lambdaEquality
Latex:
\mforall{}[x:Top]. \mforall{}[f:a:Top fp-> Top]. \mforall{}[g,eq:Top]. (x \mmember{} dom(g o f) \msim{} x \mmember{} dom(f))
Date html generated:
2018_05_21-PM-09_27_44
Last ObjectModification:
2018_02_09-AM-10_23_17
Theory : finite!partial!functions
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